In general, the prior art method of providing a game racket handle with a shock-absorbing means involves the use of an elastic shock-absorbing material, which is located securely in a space between the shaft and the hand grip, as exemplified by the U.S. Pat. No. 4,203,596. The prior art method mentioned above is defective in that the shock-absorbing means can not attenuate effectively the axially-transmitted vibrational force of the shaft, and that most of the vibrational force is therefore transmitted to the hand grip, thereby subjecting a player's hand holding the game racket to an injury caused by the shock wave. Another U.S. Pat. No. 5,131,652 discloses a game racket having a shaft which is mounted in a hand grip such that there is a clearance between the outer wall surface of the shaft and the inner wall surface of the hand grip. The clearance serves the purpose of preventing the vibrational energy of the shaft from transmitting to the hand grip. The "clearance method" described above is effective in preventing the transmission of the shock wave from the shaft to the hand grip. However, it occurs from time to time that a player makes an effort to return a fast ball in a desperate manner that the head frame of the game racket hits hard accidentally the ground, as illustrated in FIG. 4. When such an incident takes place, the force of impact exerting on the shaft can be transmitted from the shaft to the hand grip, thereby causing an injury to a player's hand holding the hand grip. In addition, the game racket handle disclosed in the above-mentioned U.S. Pat. No. 5,131,652 is defective in design in that its shaft and hand grip are located axially in the handle in a confinement manner.